Self-weight and seismic instability of a Qin Terracotta Army horse using finite element analysis
This study utilizes finite element analysis on a 3D-scanned model of a Qin Terracotta Army horse to demonstrate that while self-weight and frequent earthquakes cause minimal damage, rare earthquakes induce global sliding and overturning instability, with friction and ground motion type significantly influencing the response but shell thickness variations having negligible impact on the dominant failure modes.
Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer
The ancient world is filled with objects that have survived for millennia, yet their greatest threat often comes not from time itself, but from the sudden, violent shaking of the earth. For large, freestanding statues made of heavy clay, an earthquake presents a unique mechanical puzzle. Unlike a building, which is anchored to the ground, a statue stands on its own feet. When the ground moves, the statue does not necessarily move with it; instead, it may slide across the floor, rock back and forth on its base, or tip over completely. Predicting which of these fates awaits a specific object requires understanding three things: how heavy it is, where its weight is concentrated, and how much friction exists between its feet and the surface it stands on. This is the core challenge of protecting fragile heritage sites in seismically active regions, where the goal is to keep these silent witnesses of history standing tall when the ground beneath them begins to tremble.
In the heart of Shaanxi Province, China, lies the Mausoleum of the First Qin Emperor, home to the famous Terracotta Army. Among the thousands of life-sized warriors and horses, the horses present a particularly difficult case for conservation. They are tall, hollow, and balanced on four slender legs, making them inherently less stable than the human figures. A team of researchers from Beijing University of Civil Engineering and Architecture and the Emperor Qinshihuang's Mausoleum Site Museum decided to investigate exactly how a single terracotta horse would behave during an earthquake. They did not shake a real artifact, which would be far too risky, but instead created a precise digital twin of a restored horse from Pit 1. By feeding this virtual model into a computer program capable of simulating physics, they could watch how the horse reacted to different types of ground shaking, different levels of friction, and different directions of force, all without ever touching the fragile clay.
The researchers began by scanning a real, restored horse, cataloged as T23G9:C2④, which stands about 1.7 meters tall and weighs roughly 332 kilograms. Using a handheld laser scanner, they captured millions of points to create a three-dimensional map of the horse's surface. They then translated this map into a computer model made of thousands of tiny triangular shells, effectively wrapping the horse in a digital skin that mimicked its actual hollow structure and varying thickness. To ensure the model was accurate, they adjusted the thickness of this digital skin until the computer's version of the horse weighed exactly the same as the real one. They then subjected this digital horse to a series of virtual earthquakes, using two different types of ground motion records: one based on a famous historical earthquake in California and another generated by computer to match the specific soil conditions of the museum site. They tested these motions at two intensity levels: a frequent, moderate tremor and a rare, catastrophic one.
What the simulations revealed was a story of direction and balance. When the ground shook gently, the horse barely moved, shifting only a few millimeters before settling back into place. However, when the virtual ground shook with the force of a major earthquake, the outcome depended entirely on which way the shaking came from. If the ground moved side-to-side, perpendicular to the horse's head and tail, the horse became unstable and tipped over. In these scenarios, the horse would rock violently and eventually fall, a fate that occurred in the simulations regardless of how rough or smooth the surface beneath it was. The researchers found that the horse is simply too top-heavy and narrow in this direction to resist a strong sideways push.
In contrast, when the ground shook along the horse's length, from nose to tail, the horse did not tip over. Instead, it slid. The simulations showed that the horse would skid across the floor, sometimes moving nearly half a meter, but it would remain upright. The type of ground motion mattered here as well; the computer-generated earthquake, which lasted longer, caused the horse to slide much farther than the historical California record did. The friction between the horse's feet and the floor changed how quickly it slid and how much it rocked, but it could not stop the sliding entirely. Crucially, in every single scenario where the horse slid or tipped, the clay itself did not crack. The internal stresses generated by the movement never reached the breaking point of the terracotta material. The danger was not that the horse would shatter into pieces, but that it would fall or be dragged across the floor.
The study also checked whether the way they modeled the horse's thickness might have skewed the results. They ran the simulations again with the digital skin made slightly thinner and slightly thicker, representing a twenty percent variation in the horse's actual wall thickness. The outcome remained the same: the horse still tipped over in the side-to-side direction and slid in the lengthwise direction. This confirmed that the primary risks are global instability—falling or sliding—rather than the material breaking under stress. The findings suggest that protecting these ancient horses requires a strategy focused on preventing them from tipping over sideways and stopping them from sliding long distances, rather than worrying about the clay cracking from the vibration itself. For the curators and engineers tasked with preserving these treasures, the lesson is clear: the orientation of the horse matters, and the floor beneath it must be designed to hold firm against the specific ways the earth is most likely to move.
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